Gold Alignment and Internal Dissipation

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Abstract
The measures of mechanical alignment are obtained for both prolate and oblate grains whose temperatures are comparable to the grain kinetic energy divided by k, the Boltzmann constant. For such grains, the alignment of angular momentum, J, with the axis of maximal inertia, a, is only partial, which substantially alters the mechanical alignment as compared with the results obtained by Lazarian and Roberge, Hanany, & Messinger under the assumption of perfect alignment. We also describe Gold alignment when the Barnett dissipation is suppressed and derive an analytical expression that relates the measure of alignment to the parameters of grain nonsphericity and the direction of the gas-grain drift. This solution provides the lower limit for the measure of alignment, while the upper limit is given by the method derived by Lazarian. Using the results of a recent study of incomplete internal relaxation by Lazarian & Roberge, we find measures of alignment for the whole range of ratios of grain rotational energy to kTs, where Ts is the grain temperature. To describe alignment for mildly supersonic drifts, we suggest an analytical approach that provides good correspondence with the results of direct numerical simulations by Roberge, Hanany, & Messinger. We also extend our approach to account for simultaneous action of the Gold and Davis-Greenstein mechanisms.
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